Recurrence Quantitative Analysis of Wavelet-Based Surrogate Data for Nonlinearity Testing in Heart Rate Variability

Abstract

Exploring the presence of nonlinearity through surrogate data testing provides insights into the nature of physical and biological systems like those obtained from heart rate variability (HRV). Short-term HRV time series are of great clinical interest to study autonomic impairments manifested in chronic diseases such as the end stage renal disease (ESRD) and the response of patients to treatment with hemodialysis (HD). In contrast to Iterative Amplitude Adjusted Fourier Transform (IAAFT), the Pinned Wavelet Iterative Amplitude Adjusted Fourier Transform (PWIAAFT) surrogates preserve nonstationary behavior in time series, a common characteristic of HRV. We aimed to test synthetic data and HRV time series for the existence of nonlinearity. Recurrence Quantitative Analysis (RQA) indices were used as discriminative statistics in IAAFT and PWIAAFT surrogates of linear stationary and nonstationary processes. HRV time series of healthy subjects and 29 ESRD patients before and after HD were tested in this setting during an active standing test. Contrary to PWIAAFT, linear nonstationary time series may be erroneously regarded as nonlinear according to the IAAFT surrogates. Here, a lower proportion of HRV time series was classified as nonlinear with PWIAAFT, compared to IAAFT, confirming that the nonstationarity condition influences the testing of nonlinear behavior in HRV. A contribution of nonlinearity was found in the HRV data of healthy individuals. A lower proportion of nonlinear time series was also found in ESRD patients, but statistical significance was not found. Although this proportion tends to be lower in ESRD patients, as much as 60% of time series proved to be nonlinear in healthy subjects. Given the important contribution of nonlinearity in HRV data, a nonlinear point of view is required to achieve a broader understanding of cardiovascular physiology.

Characterization of heart rate variability in end-stage renal disease patients after kidney transplantation with recurrence quantification analysis

“…In previous works, the SDNN of ESRD patients before hemodialysis treatment did not change significantly from a supine position to active standing [ 7 ]. In this study, patients after kidney transplantation display a significant decrease in SDNN after active standing, as expected in healthy subjects [ 13 ]. Regarding RQA measures, ESRD patients treated with hemodialysis do not show a statistically significant change in response to the active standing test (laminarity, trapping time, and T2) [ 7 ].…”

“…I other studies, it has been observed that the SDNN increases largely after kidney transplantation [ 12 ]. Furthermore, kidney transplant recipients without diabetes have been observed to have a larger standard deviation of 5-minute heartbeat intervals within a 24-hour period compared to recipients with diabetes [ 13 ]. To compare appropriately in this work, the potential improvement after kidney transplantation should be compared with the HRV indices in the same subjects before and after transplantation.…”

“…It is expected that linear [ 1 ] and RQA measures [ 11 , 13 ] change in healthy subjects in response to active standing, given that the rapid changes in heart rate dynamics are mainly attributed to an autonomic response [ 11 ]. The lack of a significant response in ESRD maybe is due to autonomic nervous system impairment (dysautonomia), as is supported by experimental and observational studies [ 3 ], although more factors could be involved.…”

Nonlinear Dynamics of Heart Rate Variability after Acutely Induced Myocardial Ischemia by Percutaneous Transluminal Coronary Angioplasty

“…This method was used in 5-min HRV time series in a previous work [ 12 ] where no benefit was found from using a threshold for wavelet fixation ρ > 0.01. Therefore, in this work we use ρ = 0.01.…”

“…To overcome this issue, it has been proposed to use methods based on wavelet decomposition to generate surrogate data that preserve nonstationary behavior of time series [ 10 , 11 ]. We have implemented such methods in short-term HRV of healthy subjects and in pathologic conditions [ 12 ], in which we propose to study nonlinear behavior through recurrence quantification analysis (RQA). This approach is suitable for short, noisy, and nonstationary time series [ 13 ], properties that are present in HRV.…”